Resonant enhancement of MQT in Josephson junctions: the influence of coherent two-level systems

We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature $T_{cr}$ between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux $\mathrm{\Phi }$. Beyond that we predict a narrow peak in the dependence of $T_{cr}(\mathrm{\Phi })$ occurring in the intermediate range of $\mathrm{\Phi }$. The effect becomes more pronounced as the junction size increases. We explain this effect quantitatively by a strong resonant suppression of a potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.